5L 2s
↖4L 1s | ↑5L 1s | 6L 1s↗ |
←4L 2s | 5L 2s | 6L 2s→ |
↙4L 3s | ↓5L 3s | 6L 3s↘ |
5L 2s, named diatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 685.7¢ to 720¢, or from 480¢ to 514.3¢.
The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps – denoted as L's and s's – represent whole number step sizes, thus producing different edos. These step ratios affect the sizes of the diatonic scale's intervals and correspond to different tuning systems.
Among the most well-known forms of this scale are the diatonic scale of 12edo, the Pythagorean diatonic scale, and scales produced by meantone systems.
Name
TAMNAMS suggests the temperament-agnostic name diatonic for this scale, which commonly refers to a scale with 5 whole steps and 2 half steps. See TAMNAMS/Appendix#On_the_term_diatonic for further clarification.
Notation
- This article assumes TAMNAMS for naming step ratios.
Intervals
Intervals are identical to that of standard notation. As such, the usual interval qualities of major/minor and augmented/perfect/diminished apply here.
Intervals (with relation to root) | Size | Abbrev. | ||
---|---|---|---|---|
Generic | Specific | L's and s's | Range in cents | |
0-diastep (root) | Perfect 0-diastep | 0 | 0.0¢ | P0ms |
1-diastep | Minor 1-diastep | s | 0.0¢ to 171.4¢ | m1ms |
Major 1-diastep | L | 171.4¢ to 240.0¢ | M1ms | |
2-diastep | Minor 2-diastep | L + s | 240.0¢ to 342.9¢ | m2ms |
Major 2-diastep | 2L | 342.9¢ to 480.0¢ | M2ms | |
3-diastep | Perfect 3-diastep | 2L + s | 480.0¢ to 514.3¢ | P3ms |
Augmented 3-diastep | 3L | 514.3¢ to 720.0¢ | A3ms | |
4-diastep | Diminished 4-diastep | 2L + 2s | 480.0¢ to 685.7¢ | d4ms |
Perfect 4-diastep | 3L + s | 685.7¢ to 720.0¢ | P4ms | |
5-diastep | Minor 5-diastep | 3L + 2s | 720.0¢ to 857.1¢ | m5ms |
Major 5-diastep | 4L + s | 857.1¢ to 960.0¢ | M5ms | |
6-diastep | Minor 6-diastep | 4L + 2s | 960.0¢ to 1028.6¢ | m6ms |
Major 6-diastep | 5L + s | 1028.6¢ to 1200.0¢ | M6ms | |
7-diastep (octave) | Perfect 7-diastep | 5L + 2s | 1200.0¢ | P7ms |
Note names
Note names are identical to that of standard notation. Thus, the basic gamut for 5L 2s is the following:
C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B, C
Theory
Temperament interpretations
- Main article: 5L 2s/Temperaments
5L 2s has several rank-2 temperament interpretations, such as:
- Meantone, with generators around 696.2¢. This includes:
- Flattone, with generators around 693.7¢.
- Schismic, with generators around 702¢.
- Parapyth, with generators around 704.7¢.
- Archy, with generators around 709.3¢. This includes:
- Supra, with generators around 707.2¢
- Superpyth, with generators around 710.3¢
- Ultrapyth, with generators around 713.7¢.
Tuning ranges
Simple tunings
17edo and 19edo are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
Scale degree | 12edo (Basic, L:s = 2:1) | 17edo (Hard, L:s = 3:1) | 19edo (Soft, L:s = 3:2) | Approx. JI Ratios | |||
---|---|---|---|---|---|---|---|
Steps | Cents | Steps | Cents | Steps | Cents | ||
Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
Minor 1-diadegree | 1 | 100 | 1 | 70.6 | 2 | 126.3 | |
Major 1-diadegree | 2 | 200 | 3 | 211.8 | 3 | 189.5 | |
Minor 2-diadegree | 3 | 300 | 4 | 282.4 | 5 | 315.8 | |
Major 2-diadegree | 4 | 400 | 6 | 423.5 | 6 | 378.9 | |
Perfect 3-diadegree | 5 | 500 | 7 | 494.1 | 8 | 505.3 | |
Augmented 3-diadegree | 6 | 600 | 9 | 635.3 | 9 | 568.4 | |
Diminished 4-diadegree | 6 | 600 | 8 | 564.7 | 10 | 631.6 | |
Perfect 4-diadegree | 7 | 700 | 10 | 705.9 | 11 | 694.7 | |
Minor 5-diadegree | 8 | 800 | 11 | 776.5 | 13 | 821.1 | |
Major 5-diadegree | 9 | 900 | 13 | 917.6 | 14 | 884.2 | |
Minor 6-diadegree | 10 | 1000 | 14 | 988.2 | 16 | 1010.5 | |
Major 6-diadegree | 11 | 1100 | 16 | 1129.4 | 17 | 1073.7 | |
Perfect 7-diadegree (octave) | 12 | 1200 | 17 | 1200 | 19 | 1200 | 2/1 (exact) |
Ultrasoft tunings
Scale degree | 26edo (Supersoft, L:s = 4:3) | 7edo (Equalized, L:s = 1:1) | 33edo (L:s = 5:4) | 40edo (L:s = 6:5) | Approx. JI Ratios | ||||
---|---|---|---|---|---|---|---|---|---|
Steps | Cents | Steps | Cents | Steps | Cents | Steps | Cents | ||
Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
Minor 1-diadegree | 3 | 138.5 | 1 | 171.4 | 4 | 145.5 | 5 | 150 | |
Major 1-diadegree | 4 | 184.6 | 1 | 171.4 | 5 | 181.8 | 6 | 180 | |
Minor 2-diadegree | 7 | 323.1 | 2 | 342.9 | 9 | 327.3 | 11 | 330 | |
Major 2-diadegree | 8 | 369.2 | 2 | 342.9 | 10 | 363.6 | 12 | 360 | |
Perfect 3-diadegree | 11 | 507.7 | 3 | 514.3 | 14 | 509.1 | 17 | 510 | |
Augmented 3-diadegree | 12 | 553.8 | 3 | 514.3 | 15 | 545.5 | 18 | 540 | |
Diminished 4-diadegree | 14 | 646.2 | 4 | 685.7 | 18 | 654.5 | 22 | 660 | |
Perfect 4-diadegree | 15 | 692.3 | 4 | 685.7 | 19 | 690.9 | 23 | 690 | |
Minor 5-diadegree | 18 | 830.8 | 5 | 857.1 | 23 | 836.4 | 28 | 840 | |
Major 5-diadegree | 19 | 876.9 | 5 | 857.1 | 24 | 872.7 | 29 | 870 | |
Minor 6-diadegree | 22 | 1015.4 | 6 | 1028.6 | 28 | 1018.2 | 34 | 1020 | |
Major 6-diadegree | 23 | 1061.5 | 6 | 1028.6 | 29 | 1054.5 | 35 | 1050 | |
Perfect 7-diadegree (octave) | 26 | 1200 | 7 | 1200 | 33 | 1200 | 40 | 1200 | 2/1 (exact) |
Parasoft tunings
- See also: Flattone
Parasoft diatonic tunings (4:3 to 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths (3/2, flat of 702¢) to produce major 3rds that are flatter than 5/4 (386¢).
Edos include 19edo, 26edo, 45edo, and 64edo.
Scale degree | 19edo (Soft, L:s = 3:2) | 26edo (Supersoft, L:s = 4:3) | 45edo (L:s = 7:5) | 64edo (L:s = 10:7) | Approx. JI Ratios | ||||
---|---|---|---|---|---|---|---|---|---|
Steps | Cents | Steps | Cents | Steps | Cents | Steps | Cents | ||
Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
Minor 1-diadegree | 2 | 126.3 | 3 | 138.5 | 5 | 133.3 | 7 | 131.3 | |
Major 1-diadegree | 3 | 189.5 | 4 | 184.6 | 7 | 186.7 | 10 | 187.5 | |
Minor 2-diadegree | 5 | 315.8 | 7 | 323.1 | 12 | 320 | 17 | 318.8 | |
Major 2-diadegree | 6 | 378.9 | 8 | 369.2 | 14 | 373.3 | 20 | 375 | |
Perfect 3-diadegree | 8 | 505.3 | 11 | 507.7 | 19 | 506.7 | 27 | 506.2 | |
Augmented 3-diadegree | 9 | 568.4 | 12 | 553.8 | 21 | 560 | 30 | 562.5 | |
Diminished 4-diadegree | 10 | 631.6 | 14 | 646.2 | 24 | 640 | 34 | 637.5 | |
Perfect 4-diadegree | 11 | 694.7 | 15 | 692.3 | 26 | 693.3 | 37 | 693.8 | |
Minor 5-diadegree | 13 | 821.1 | 18 | 830.8 | 31 | 826.7 | 44 | 825 | |
Major 5-diadegree | 14 | 884.2 | 19 | 876.9 | 33 | 880 | 47 | 881.2 | |
Minor 6-diadegree | 16 | 1010.5 | 22 | 1015.4 | 38 | 1013.3 | 54 | 1012.5 | |
Major 6-diadegree | 17 | 1073.7 | 23 | 1061.5 | 40 | 1066.7 | 57 | 1068.8 | |
Perfect 7-diadegree (octave) | 19 | 1200 | 26 | 1200 | 45 | 1200 | 64 | 1200 | 2/1 (exact) |
Hyposoft tunings
- See also: Meantone
Hyposoft diatonic tunings (3:2 to 2:1) correspond to meantone temperaments, characterized by flattened perfect 5ths (flat of 702¢) to produce diatonic major 3rds that approximate 5/4 (386¢).
Edos include 19edo, 31edo, 43edo, and 50edo.
Scale degree | 19edo (Soft, L:s = 3:2) | 31edo (Semisoft, L:s = 5:3) | 43edo (L:s = 7:4) | 50edo (L:s = 8:5) | Approx. JI Ratios | ||||
---|---|---|---|---|---|---|---|---|---|
Steps | Cents | Steps | Cents | Steps | Cents | Steps | Cents | ||
Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
Minor 1-diadegree | 2 | 126.3 | 3 | 116.1 | 4 | 111.6 | 5 | 120 | |
Major 1-diadegree | 3 | 189.5 | 5 | 193.5 | 7 | 195.3 | 8 | 192 | |
Minor 2-diadegree | 5 | 315.8 | 8 | 309.7 | 11 | 307 | 13 | 312 | |
Major 2-diadegree | 6 | 378.9 | 10 | 387.1 | 14 | 390.7 | 16 | 384 | |
Perfect 3-diadegree | 8 | 505.3 | 13 | 503.2 | 18 | 502.3 | 21 | 504 | |
Augmented 3-diadegree | 9 | 568.4 | 15 | 580.6 | 21 | 586 | 24 | 576 | |
Diminished 4-diadegree | 10 | 631.6 | 16 | 619.4 | 22 | 614 | 26 | 624 | |
Perfect 4-diadegree | 11 | 694.7 | 18 | 696.8 | 25 | 697.7 | 29 | 696 | |
Minor 5-diadegree | 13 | 821.1 | 21 | 812.9 | 29 | 809.3 | 34 | 816 | |
Major 5-diadegree | 14 | 884.2 | 23 | 890.3 | 32 | 893 | 37 | 888 | |
Minor 6-diadegree | 16 | 1010.5 | 26 | 1006.5 | 36 | 1004.7 | 42 | 1008 | |
Major 6-diadegree | 17 | 1073.7 | 28 | 1083.9 | 39 | 1088.4 | 45 | 1080 | |
Perfect 7-diadegree (octave) | 19 | 1200 | 31 | 1200 | 43 | 1200 | 50 | 1200 | 2/1 (exact) |
Hypohard tunings
- See also: Pythagorean tuning and schismatic temperament
The range of hypohard tunings can be divided into a minihard range (2:1 to 5:2) and quasihard range (5:2 to 3:1).
Minihard tunings
Minihard diatonic tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in a major 3rd of 81/64 (407¢).
Scale degree | 41edo (L:s = 7:3) | 53edo (L:s = 9:4) | Approx. JI Ratios | ||
---|---|---|---|---|---|
Steps | Cents | Steps | Cents | ||
Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 1/1 (exact) |
Minor 1-diadegree | 3 | 87.8 | 4 | 90.6 | |
Major 1-diadegree | 7 | 204.9 | 9 | 203.8 | |
Minor 2-diadegree | 10 | 292.7 | 13 | 294.3 | |
Major 2-diadegree | 14 | 409.8 | 18 | 407.5 | |
Perfect 3-diadegree | 17 | 497.6 | 22 | 498.1 | |
Augmented 3-diadegree | 21 | 614.6 | 27 | 611.3 | |
Diminished 4-diadegree | 20 | 585.4 | 26 | 588.7 | |
Perfect 4-diadegree | 24 | 702.4 | 31 | 701.9 | |
Minor 5-diadegree | 27 | 790.2 | 35 | 792.5 | |
Major 5-diadegree | 31 | 907.3 | 40 | 905.7 | |
Minor 6-diadegree | 34 | 995.1 | 44 | 996.2 | |
Major 6-diadegree | 38 | 1112.2 | 49 | 1109.4 | |
Perfect 7-diadegree (octave) | 41 | 1200 | 53 | 1200 | 2/1 (exact) |
Quasihard tunings
Quasihard diatonic tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of 32/27 (294¢).
Edos include 17edo, 29edo, and 46edo. 17edo is considered to be on the sharper end of the neogothic spectrum, with a major 3rd that is more discordant than flatter neogothic tunings.
Scale degree | 17edo (Hard, L:s = 3:1) | 29edo (Semihard, L:s = 5:2) | 46edo (L:s = 8:3) | Approx. JI Ratios | |||
---|---|---|---|---|---|---|---|
Steps | Cents | Steps | Cents | Steps | Cents | ||
Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
Minor 1-diadegree | 1 | 70.6 | 2 | 82.8 | 3 | 78.3 | |
Major 1-diadegree | 3 | 211.8 | 5 | 206.9 | 8 | 208.7 | |
Minor 2-diadegree | 4 | 282.4 | 7 | 289.7 | 11 | 287 | |
Major 2-diadegree | 6 | 423.5 | 10 | 413.8 | 16 | 417.4 | |
Perfect 3-diadegree | 7 | 494.1 | 12 | 496.6 | 19 | 495.7 | |
Augmented 3-diadegree | 9 | 635.3 | 15 | 620.7 | 24 | 626.1 | |
Diminished 4-diadegree | 8 | 564.7 | 14 | 579.3 | 22 | 573.9 | |
Perfect 4-diadegree | 10 | 705.9 | 17 | 703.4 | 27 | 704.3 | |
Minor 5-diadegree | 11 | 776.5 | 19 | 786.2 | 30 | 782.6 | |
Major 5-diadegree | 13 | 917.6 | 22 | 910.3 | 35 | 913 | |
Minor 6-diadegree | 14 | 988.2 | 24 | 993.1 | 38 | 991.3 | |
Major 6-diadegree | 16 | 1129.4 | 27 | 1117.2 | 43 | 1121.7 | |
Perfect 7-diadegree (octave) | 17 | 1200 | 29 | 1200 | 46 | 1200 | 2/1 (exact) |
Parahard and ultrahard tunings
- See also: Archy
Parahard (3:1 to 4:1) and ultrahard (4:1 to 1:0) diatonic tunings correspond to archy systems, with perfect 5ths that are significantly sharper than than 702¢.
Edos include 17edo, 22edo, 27edo, and 32edo, among others.
Scale degree | 17edo (Hard, L:s = 3:1) | 22edo (Superhard, L:s = 4:1) | 27edo (L:s = 5:1) | 32edo (L:s = 6:1) | Approx. JI Ratios | ||||
---|---|---|---|---|---|---|---|---|---|
Steps | Cents | Steps | Cents | Steps | Cents | Steps | Cents | ||
Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
Minor 1-diadegree | 1 | 70.6 | 1 | 54.5 | 1 | 44.4 | 1 | 37.5 | |
Major 1-diadegree | 3 | 211.8 | 4 | 218.2 | 5 | 222.2 | 6 | 225 | |
Minor 2-diadegree | 4 | 282.4 | 5 | 272.7 | 6 | 266.7 | 7 | 262.5 | |
Major 2-diadegree | 6 | 423.5 | 8 | 436.4 | 10 | 444.4 | 12 | 450 | |
Perfect 3-diadegree | 7 | 494.1 | 9 | 490.9 | 11 | 488.9 | 13 | 487.5 | |
Augmented 3-diadegree | 9 | 635.3 | 12 | 654.5 | 15 | 666.7 | 18 | 675 | |
Diminished 4-diadegree | 8 | 564.7 | 10 | 545.5 | 12 | 533.3 | 14 | 525 | |
Perfect 4-diadegree | 10 | 705.9 | 13 | 709.1 | 16 | 711.1 | 19 | 712.5 | |
Minor 5-diadegree | 11 | 776.5 | 14 | 763.6 | 17 | 755.6 | 20 | 750 | |
Major 5-diadegree | 13 | 917.6 | 17 | 927.3 | 21 | 933.3 | 25 | 937.5 | |
Minor 6-diadegree | 14 | 988.2 | 18 | 981.8 | 22 | 977.8 | 26 | 975 | |
Major 6-diadegree | 16 | 1129.4 | 21 | 1145.5 | 26 | 1155.6 | 31 | 1162.5 | |
Perfect 7-diadegree (octave) | 17 | 1200 | 22 | 1200 | 27 | 1200 | 32 | 1200 | 2/1 (exact) |
Modes
Diatonic modes have standard names from classical music theory.
UDP | Rotational order | Step pattern | Mode names |
---|---|---|---|
6|0 | 1 | LLLsLLs | Lydian |
5|1 | 5 | LLsLLLs | Ionian (major) |
4|2 | 2 | LLsLLsL | Mixolydian |
3|3 | 6 | LsLLLsL | Dorian |
2|4 | 3 | LsLLsLL | Aeolian (minor) |
1|5 | 7 | sLLLsLL | Phrygian |
0|6 | 4 | sLLsLLL | Locrian |
Each mode has the following scale degrees, reached by raising or lowering certain naturals by a chroma.
Mode | Scale degree (on C) | ||||||||
---|---|---|---|---|---|---|---|---|---|
UDP | Step pattern | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th |
6|0 | LLLsLLs | Perfect (C) | Major (D) | Major (E) | Augmented (F#) | Perfect (G) | Major (A) | Major (B) | Perfect (C) |
5|1 | LLsLLLs | Perfect (C) | Major (D) | Major (E) | Perfect (F) | Perfect (G) | Major (A) | Major (B) | Perfect (C) |
4|2 | LLsLLsL | Perfect (C) | Major (D) | Major (E) | Perfect (F) | Perfect (G) | Major (A) | Minor (Bb) | Perfect (C) |
3|3 | LsLLLsL | Perfect (C) | Major (D) | Minor (Eb) | Perfect (F) | Perfect (G) | Major (A) | Minor (Bb) | Perfect (C) |
2|4 | LsLLsLL | Perfect (C) | Major (D) | Minor (Eb) | Perfect (F) | Perfect (G) | Minor (Ab) | Minor (Bb) | Perfect (C) |
1|5 | sLLLsLL | Perfect (C) | Minor (Db) | Minor (Eb) | Perfect (F) | Perfect (G) | Minor (Ab) | Minor (Bb) | Perfect (C) |
0|6 | sLLsLLL | Perfect (C) | Minor (Db) | Minor (Eb) | Perfect (F) | Diminished (Gb) | Minor (Ab) | Minor (Bb) | Perfect (C) |
Scales
Subset and superset scales
5L 2s has a parent scale of 2L 3s, a pentatonic scale, meaning 2L 3s is a subset. 5L 2s also has two child scales, which are supersets of 5L 2s:
- 7L 5s, a chromatic scale produced using soft-of-basic step ratios.
- 5L 7s, a chromatic scale produced using hard-of-basic step ratios.
12edo, the equalized form of both 7L 5s and 5L 7s, is also a superset of 5L 2s.
MODMOS scales and muddles
- Main article: 5L 2s MODMOSes and 5L 2s Muddles
Scala files
- Meantone7 – 19edo and 31edo tunings
- Nestoria7 – 171edo tuning
- Pythagorean7 – Pythagorean tuning
- Garibaldi7 – 94edo tuning
- Cotoneum7 – 217edo tuning
- Edson7 – 29edo tuning
- Pepperoni7 – 271edo tuning
- Supra7 – 56edo tuning
- Archy7 – 472edo tuning
Scale tree
Generator (in steps of edo) | Cents | Step ratio | Comments | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | ||||||||
4\7 | 685.714 | 514.286 | 1:1 | 1.000 | Equalized 5L 2s | ||||||
27\47 | 689.362 | 510.638 | 7:6 | 1.167 | |||||||
23\40 | 690.000 | 510.000 | 6:5 | 1.200 | |||||||
42\73 | 690.411 | 509.589 | 11:9 | 1.222 | |||||||
19\33 | 690.909 | 509.091 | 5:4 | 1.250 | |||||||
53\92 | 691.304 | 508.696 | 14:11 | 1.273 | |||||||
34\59 | 691.525 | 508.475 | 9:7 | 1.286 | |||||||
49\85 | 691.765 | 508.235 | 13:10 | 1.300 | |||||||
15\26 | 692.308 | 507.692 | 4:3 | 1.333 | Supersoft 5L 2s | ||||||
56\97 | 692.784 | 507.216 | 15:11 | 1.364 | |||||||
41\71 | 692.958 | 507.042 | 11:8 | 1.375 | |||||||
67\116 | 693.103 | 506.897 | 18:13 | 1.385 | |||||||
26\45 | 693.333 | 506.667 | 7:5 | 1.400 | Flattone is in this region | ||||||
63\109 | 693.578 | 506.422 | 17:12 | 1.417 | |||||||
37\64 | 693.750 | 506.250 | 10:7 | 1.429 | |||||||
48\83 | 693.976 | 506.024 | 13:9 | 1.444 | |||||||
11\19 | 694.737 | 505.263 | 3:2 | 1.500 | Soft 5L 2s | ||||||
51\88 | 695.455 | 504.545 | 14:9 | 1.556 | |||||||
40\69 | 695.652 | 504.348 | 11:7 | 1.571 | |||||||
69\119 | 695.798 | 504.202 | 19:12 | 1.583 | |||||||
29\50 | 696.000 | 504.000 | 8:5 | 1.600 | |||||||
76\131 | 696.183 | 503.817 | 21:13 | 1.615 | Golden meantone (696.2145¢) | ||||||
47\81 | 696.296 | 503.704 | 13:8 | 1.625 | |||||||
65\112 | 696.429 | 503.571 | 18:11 | 1.636 | |||||||
18\31 | 696.774 | 503.226 | 5:3 | 1.667 | Semisoft 5L 2s Meantone is in this region | ||||||
61\105 | 697.143 | 502.857 | 17:10 | 1.700 | |||||||
43\74 | 697.297 | 502.703 | 12:7 | 1.714 | |||||||
68\117 | 697.436 | 502.564 | 19:11 | 1.727 | |||||||
25\43 | 697.674 | 502.326 | 7:4 | 1.750 | |||||||
57\98 | 697.959 | 502.041 | 16:9 | 1.778 | |||||||
32\55 | 698.182 | 501.818 | 9:5 | 1.800 | |||||||
39\67 | 698.507 | 501.493 | 11:6 | 1.833 | |||||||
7\12 | 700.000 | 500.000 | 2:1 | 2.000 | Basic 5L 2s Scales with tunings softer than this are proper | ||||||
38\65 | 701.538 | 498.462 | 11:5 | 2.200 | |||||||
31\53 | 701.887 | 498.113 | 9:4 | 2.250 | The generator closest to a just 3/2 for EDOs less than 200 | ||||||
55\94 | 702.128 | 497.872 | 16:7 | 2.286 | Garibaldi / Cassandra | ||||||
24\41 | 702.439 | 497.561 | 7:3 | 2.333 | |||||||
65\111 | 702.703 | 497.297 | 19:8 | 2.375 | |||||||
41\70 | 702.857 | 497.143 | 12:5 | 2.400 | |||||||
58\99 | 703.030 | 496.970 | 17:7 | 2.429 | |||||||
17\29 | 703.448 | 496.552 | 5:2 | 2.500 | Semihard 5L 2s | ||||||
61\104 | 703.846 | 496.154 | 18:7 | 2.571 | |||||||
44\75 | 704.000 | 496.000 | 13:5 | 2.600 | |||||||
71\121 | 704.132 | 495.868 | 21:8 | 2.625 | Golden neogothic (704.0956¢) | ||||||
27\46 | 704.348 | 495.652 | 8:3 | 2.667 | Neogothic is in this region | ||||||
64\109 | 704.587 | 495.413 | 19:7 | 2.714 | |||||||
37\63 | 704.762 | 495.238 | 11:4 | 2.750 | |||||||
47\80 | 705.000 | 495.000 | 14:5 | 2.800 | |||||||
10\17 | 705.882 | 494.118 | 3:1 | 3.000 | Hard 5L 2s | ||||||
43\73 | 706.849 | 493.151 | 13:4 | 3.250 | |||||||
33\56 | 707.143 | 492.857 | 10:3 | 3.333 | |||||||
56\95 | 707.368 | 492.632 | 17:5 | 3.400 | |||||||
23\39 | 707.692 | 492.308 | 7:2 | 3.500 | |||||||
59\100 | 708.000 | 492.000 | 18:5 | 3.600 | |||||||
36\61 | 708.197 | 491.803 | 11:3 | 3.667 | |||||||
49\83 | 708.434 | 491.566 | 15:4 | 3.750 | |||||||
13\22 | 709.091 | 490.909 | 4:1 | 4.000 | Superhard 5L 2s Archy is in this region | ||||||
42\71 | 709.859 | 490.141 | 13:3 | 4.333 | |||||||
29\49 | 710.204 | 489.796 | 9:2 | 4.500 | |||||||
45\76 | 710.526 | 489.474 | 14:3 | 4.667 | |||||||
16\27 | 711.111 | 488.889 | 5:1 | 5.000 | |||||||
35\59 | 711.864 | 488.136 | 11:2 | 5.500 | |||||||
19\32 | 712.500 | 487.500 | 6:1 | 6.000 | |||||||
22\37 | 713.514 | 486.486 | 7:1 | 7.000 | |||||||
3\5 | 720.000 | 480.000 | 1:0 | → ∞ | Collapsed 5L 2s |
Step ratio diagram
See also
- Diatonic functional harmony
- Diatonic (disambiguation page)